Hi. I have a very long question which has 2 parts... I've worked out part 1 but part 2 is giving me problems.

Task 1

Imagine that you are the pilot of a light aircraft which is capable of cruising at a steady speed ofakm/hr in still air. You have enough fuel on board to lastbhours.

You take off from the airfield and, on the outward journey, are helped along by ackm/hr wind which increases your speed relative to the ground toa + ckm/hr.

Suddenly you realise on the return journey you will be flying into the wind and will therefore slow down toa-ckm/hr.

What is themaximum distancethat you can travel from the airfield, and still be sure that you have enough fuel left to make a safe return journey? Results must beverified.

a = 350 b = 4.5 c = 40

I found the answer to part 1 through the formula:

t = d / s by manipulating it into:

t = d / (a+c) + d / (a-c)

I subbed in the values for a, c and t and the value for a maximumone waywas 777.21 km. (1554.428km there and back).

Task 2

Determinea function linking the distance from the airfield (km) and the time of the flight (hrs). Hence,determinethegreatest distancethe plane can travel from the airfield and whatwind speedwill allow this to occur. You must demonstrate algebraic techniques and calculus. Conclusions must beverified.

Task 2... well, I'm honestly not quite sure where to start. I have derived the equation which I worked out to be:

t' = 2da^2 + 4dac + 2dc^2. That's all I've got so far... I could sub in the value of a (350), but that still leaves me with the unknowns of d, c and t.

Help would be much appreciated.

Thankyou.